Profit And Loss
Math MCQs

Question :    If a shopkeeper earns a profit of 5% by selling an article at $210, then find the cost price of that article.

Correct Answer  200

Solution & Explanation

Solution

Given, the sale price (SP) = $210

And, the profit = 5%

Then, the Cost Price (CP) = ?

Finding the cost price (CP) using formula when the SP and the profit are given

The formula to find the Cost Price, when the Sale Price (SP) and the Profit are known

Cost Price (CP) = ¹⁰⁰/_{100 + gain%} × SP

Thus, the Cost Price (CP)

= ¹⁰⁰/_{100 + 5} × 210

= ¹⁰⁰/₁₀₅ × 210 2

= 100 × 2 = 200

Thus, the Cost Price (CP) = $200 Answer

Finding the cost price (CP) using Algebraic Method when the Sale Pric (SP) and the profit are given

Given, the sale price (SP) = $210

And, the profit = 5%

Then, the Cost Price (CP) = ?

Calculation of Profit

Let the Cost Price (CP) = m

Threfore, profit = Profit% of CP

= 5% of m

= 5% × m

= ⁵/_{100 20} × m

= ¹/₂₀ × m

⇒ Profit = ^m/₂₀

Calculation of Cost Price (CP)

The Sale Price (SP) = Cost Price (CP) + Profit

⇒ 210 = m + ^m/₂₀

⇒ 210 = ^{20 m + m}/₂₀

⇒ 210 = ^{21 m}/₂₀

After cross multiplication, we get

21 m = 210 × 20

⇒ m = ^{210 × 20}/₂₁

⇒ m = ^{210 10 × 20}/₂₁

⇒ m = 10 × 20 = 200

Thus, the Cost Price (CP) = $200 Answer

Finding the cost price (CP) using Unitary Method by taking the cost price (CP) is equal to 100 when the SP and the profit are given

Given, the sale price (SP) = $210

And, the profit = 5%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 5% of 100 = 5

Thus, Sale Price (SP) = Cost Price (CP) + Profit

⇒ Sale Price (SP) = 100 + 5

⇒ Sale Price (SP) = 105

∵ If the Sale Price (SP) is 105, then the Cost Price (CP) = 100

∴ If the Sale Price (SP) is 1, then the Cost Price (CP)

= ¹⁰⁰/₁₀₅

∴ If the Sale Price (SP) is 210, then the Cost Price (CP)

= ¹⁰⁰/₁₀₅ × 210

= ¹⁰⁰/₁₀₅ × 210 2

= 100 × 2 = 200

Thus, the Cost Price (CP) = $200 Answer

Shortcut Method to find Cost Price (CP) when SP and profit are known

Given, the sale price (SP) = $210

And, the profit = 5%

Then, the Cost Price (CP) = ?

SP = CP + 5% of CP

⇒ 210 = CP + ⁵/₁₀₀ × CP

⇒ 210 = ^{100 CP + 5 CP}/₁₀₀

⇒ 210 = ^{105 CP}/₁₀₀

After cross multiplication

⇒ 210 × 100 = 105 CP

⇒ CP = ^{210 2 × 100}/₁₀₅

⇒ CP = = 2 × 100 = 200

⇒ CP = $200 Answer

Similar Questions

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(7) William loses 71% by selling an article for $988.90. For how much should he sell it to get a profit of 70%?

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